physics_135_fall_2014_lecture_1C_with_quiz - Racquetball Striking a Wall Physics for the Life Sciences Physics Tools Lecture#1C Stewart Hall Mt Etna

physics_135_fall_2014_lecture_1C_with_quiz - Racquetball...

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Physics Tools Physics for the Life Sciences Lecture #1C Racquetball Striking a Wall Mt. Etna Stewart Hall
F F . r ϕ ϕ θ
± .
The Scalar Product When we do the “scalar product” we multiply two vectors to obtain a quantity which is a pure scalar This is also called the “dot product ” or “inner product” We combine two things with magnitude and direction to get just a magnitude r F θ r F The scalar product r F is defined r F = | r | | F | cos( θ ) (magnitude of r times magnitude of F times the cosine of the angle in between) Dot product of r and F
What does this do for us? F r θ ) ) F | )
r F θ r || = r cos( θ ) r F θ F || = F cos( θ ) Note that the dot product is commutative: r F = F r = r F cos( θ ) r F θ r || = | r |cos( θ ) r F θ F || = | F |cos( θ ) Scalar Product Properties
Vector Projection and Dot Product y x ± r F ± r F r || r ± r || = r cos( ± ) r ± = r sin( ± ) ± r F F || F ± F || = F cos( ± ) F ± = F sin( ± ) F onto r r onto F r F = F r = r F cos( θ ) r dot F W = r || F = r F || W = r F = r F cos ( θ ) W = r F = r || F = r F || ²
An Example of Dot Product Given r = 10 [m], F = 100 [N], and θ = 30º, calculate the scalar product . W = r F  W = r F  = rF cos θ = (10)(100)cos(30 ° ) = 866 [mN] ± F  r ± F  r OR r F W = r F = [ + (10)cos(30 ° )](100) = 866 [mN] W = rF = [ + (100)cos(30 ° )](10) = 866 [mN] ± F  r y x z

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